{
  "abstract": "Let $p(n)$ be the ordinary partition function and let $c(n)=\\sum_{k=0}^{n-1}p(k)$, with $c(0)=0$. We prove that, for every $a\\geq1$, $b\\geq0$, and $m\\geq2$, the sequence $c(an+b)$ is not eventually constant modulo $m$, thereby answering a question posed by Chen. The proof combines the algebraicity over $\\mathbb C(j)$ of modular functions for finite-index subgroups of $\\mathrm{SL}_2(\\mathbb Z)$ with Voloch's theorem on the transcendence of elliptic modular functions in positive characteristic.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.31102",
  "author_total": 1,
  "authors": [
    {
      "name": "Kathy Q. Ji"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ej09qwtsx15pt.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.31102",
  "fulltext_url": null,
  "id": "ej09qwtsx15pt",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.31102",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2602|Advanced Mathematical Identities"
    ]
  ],
  "openalex": "W7223311263",
  "pdf_url": "https://arxiv.org/pdf/2610.31102",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ej09qwtsx15pt.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:38Z",
      "native_id": "2610.31102",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.31102"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Nonexistence of Constant Congruences for the Cumulative Partition Function",
  "title_text": "Nonexistence of Constant Congruences for the Cumulative Partition Function",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:38Z",
  "url": "https://research.draconitic.com/paper/ej09qwtsx15pt",
  "venue": "arXiv",
  "versions": []
}